Alpha particles are deflected along hyperbolic paths when they are directed towards the nuclei of gold atoms. If an alpha particle gets as close as 33 units to the nucleus along a hyperbolic path (where the nucleus is at 3 -x, 11 the center of the hyperbola) with asymptote y what is the equation of its path? Assume that it's a hyperbola that opens left and right.

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.